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Krylov Subspace Methods
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Krylov Subspace Methods: Principles and Analysis

Jörg Liesen and Zdenek Strakos

Abstract

This book offers a detailed treatment of the mathematical theory of Krylov subspace methods with focus on solving systems of linear algebraic equations. Starting from the idea of projections, Krylov subspace methods are characterised by their orthogonality and minimisation properties. Projections onto highly nonlinear Krylov subspaces can be linked with the underlying problem of moments, and therefore Krylov subspace methods can be viewed as matching moments model reduction. This allows enlightening reformulations of questions from matrix computations into the language of orthogonal polynomial ... More

Keywords: Krylov subspace methods, cost of computations, convergence analysis, conjugate gradient method, GMRES, projection methods, problem of moments, orthogonal polynomials, continued fractions, Jacobi matrices, short recurrences, cyclic invariant subspaces

Bibliographic Information

Print publication date: 2012 Print ISBN-13: 9780199655410
Published to Oxford Scholarship Online: January 2013 DOI:10.1093/acprof:oso/9780199655410.001.0001

Authors

Affiliations are at time of print publication.

Jörg Liesen, author
Professor of Numerical Mathematics, Technical University of Berlin

Zdenek Strakos, author
Professor of Mathematics, Charles University, Prague

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